Problem: Solve for $x$ and $y$ using elimination. ${-3x+y = -9}$ ${-4x-y = -33}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-7x = -42$ $\dfrac{-7x}{{-7}} = \dfrac{-42}{{-7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x+y = -9}\thinspace$ to find $y$ ${-3}{(6)}{ + y = -9}$ $-18+y = -9$ $-18{+18} + y = -9{+18}$ ${y = 9}$ You can also plug ${x = 6}$ into $\thinspace {-4x-y = -33}\thinspace$ and get the same answer for $y$ : ${-4}{(6)}{ - y = -33}$ ${y = 9}$